However, I also have an old MP4 file containing the "language": "und" metadata tag which does not cause the audio language button to appear on the iPhone. So the presence of this tag is not the cause of the button appearing.

I've been trying to figure out what causes the audio language button to be displayed for some MP4 files but not others.

Here's the FFprobe output for these two MP4 files, and the diff of them:

So my question is: how can I get FFmpeg to generate an MP4 file which does not cause the audio language button to appear on the iPhone? Maybe a metadata tag needs to be added or removed using the -metadata option?